1. Field of the Invention
The present invention generally relates to a signal analysis method. Particularly, the present invention relates to a signal analysis method for vibratory interferometry.
2. Description of the Prior Art
The conventional optical interferometric surface profilometer has been developed mainly for static measurement of nano-scale three-dimensional surface profiles. It has been widely employed for measuring surface roughness and uniformity on semiconductor wafers, depth of laser marks, metal-bump size and co-planarity during flip chip bonding, size and height of spacers in liquid-crystal display panels, and surface profile of fiber end-face and micro optical devices. In recent years, vibratory measurement has been incorporated into the optical interferometric surface profilometer, thus widening its applications in observing and measuring the vibratory behavior of functional elements and thin-films in micro-electro-mechanical system (MEMS) and micro-opto-electro-mechanical system (MOEMS) industries.
FIG. 1 is a schematic diagram showing a conventional static measurement apparatus 100, which comprises a light generator 110, a beam-splitter 120, an interferometric objective 130, an image formation unit 140 and a vertical scanner 150. This static measurement apparatus 100 can obtain the static surface profile of the object 50 under test using white-light vertical interference fringes generated, as disclosed in Taiwan Patent No. I237685.
When making a measurement, a light beam 112 generated by the light generator 110 is reflected by the beam-splitter 120 into the interferometric objective 130. The interferometric objective 130 then splits the light beam 112 into a reference light beam 112a and a measurement light beam 112b. The measurement light beam 112b is projected onto the object 50 under test and then reflected back to the interferometric objective 130. The reflected measurement light beam 112b then combines with the reference light beam 112a again to form an interfered light beam 114. The interfered light beam 114 then passes through the beam-splitter 120 into the image formation unit 140 to form an image with interference fringes.
The image formation unit 140 is a light integrator array, which can be a charge-coupled device (CCD). The intensity of the interfered light beam 114 received by any pixel of the image formation unit 140 corresponds to the interference in a specific region on the object 50 under test. The difference in optical path between the reference light beam 112a and the measurement light beam 112b is adjusted by moving the vertical scanner 150. This can control the intensity of the interfered light beam 114 for acquiring static interferometric signals, indicated by the changes in interference intensity due to differences in optical path.
FIG. 2A is a graphic representation of a static interferometric signal, where the horizontal axis corresponds to the displacement of the vertical scanner and the vertical axis corresponds to the interference intensity. FIG. 2B is a schematic diagram showing the relation between the displacement corresponding to the maximum interference intensity and the surface profile of the object under test. With reference to FIG. 1, FIG. 2A and FIG. 2B, for any region on the object 50 under test, changing the displacement of the vertical scanner 150 can acquire static interferometric signals of different intensities. Generally speaking, the position with the maximum interference intensity corresponds exactly to the height of the surface profile of the object 50 under test. In other words, the shape of the interferometric signal can be enclosed by a wave-packet, in which the exact position of the signal peak corresponds to the height of the surface profile of the object 50 under test.
When the height of the surface profile of the object 50 under test changes, the displacement of the vertical scanner 150 corresponding to the intensity of the interfered light beam 114 will also vary, thus changing the position with maximum interference intensity. Therefore, the surface profile of the object 50 under test can be obtained by measuring the exact positions where the maximum interference intensity occur for all regions on the object 50 under test.
According to the above, three-dimensional profile reconstruction using static interferometric signals begins with obtaining the exact position where the maximum interference intensity occurs for any pixel in order to calculate the height of the surface profile of the corresponding region on an object under test. Calculating the heights of all the regions on the object 50 under test yields the complete surface profile image of the object under test. In addition to surface profile image reconstruction, static interferometric signals can also be employed for measuring static characteristics of the object under test.
FIG. 3 is a schematic diagram showing a conventional vibratory measurement apparatus 300, which is similar to the static measurement apparatus 100 (shown in FIG. 1), except that it comprises in addition a strobe controller 310 and a driver plate 320. It can be used for measuring the vibratory characteristics and the surface profile of the object tested 50 under vibration.
When making the measurement, the object 50 under test is placed on the driver plate 320. The strobe controller 310 outputs signals of the same frequency into both the light generator 110 and the driver plate 320. The light generator 110 then generates a stroboscopic pulse 312 of a specific frequency, causing the driver plate 320 with the object 50 under test to vibrate at this specific frequency.
The stroboscopic pulse 312 then passes through the beam-splitter 120, the interferometric objective 130 and the object 50 under test to form an interfered light beam 314, which is fed into the image formation unit 140 to form an interference image. For any pixel of the image formation unit 140, displacement of the vertical scanner 150 will lead to changes in intensity of the interfered light beam 314. These changes due differences in optical path yield vibratory interferometric signals.
In the same way, obtaining the exact position where the maximum interference intensity occurs for a vibratory interferometric signal will give the height of the surface profile of the corresponding region on the object 50 under test; and calculating the heights of all the regions on the object 50 under test yields the complete surface profile image of the object under test. In addition to surface profile image reconstruction, vibratory interferometric signals can also be employed for measuring vibratory characteristics of the object under test.
FIG. 4A is a graphic representation of the vibration profile of an object under test and the changes in intensity of the stroboscopic pulse. With reference to FIG. 3 and as seen in FIG. 4A, the vibration cycle T of the object 50 under test is identical to a cycle of change in intensity of the stroboscopic pulse 312. There exists between the stroboscopic pulse 312 and the beginning of the vibration cycle of the object 50 under test a delay of tc, which can be adjusted arbitrarily. In general, the pulse time δT of the stroboscopic pulse 312 is much shorter than the vibration cycle T of the object 50 under test. Thus, the surface profile of the object 50 under test remains almost static during the pulse time δT when the stroboscopic pulse 312 is incident on the object 50 under test.
By using the above approach, a vibratory interferometric signal with good interference contrast can be obtained to calculate the exact position with maximum interference intensity for three-dimensional profile reconstruction for the object 50 under test in a vibrating mode.
However, with increase in vibrating frequency of the object 50 under test, the vibration cycle T of the object decreases and no longer exceeds the pulse time δT of the stroboscopic pulse 312. This leads to greater variation in the surface profile of the object 50 under test during the pulse time δT when the stroboscopic pulse 312 is incident on the object 50 under test. As a result, the interfered light beam 314 will include the interference information obtained from different positions of the vibratory surface profile of the object 50 under test. The interference contrast of the vibratory interferometric signal decreases after the interfered light beam 314 is integrated by the image formation unit 140.
FIG. 4B is a graphic representation of a vibratory interferometric signal for an object under high-frequency vibration. With reference to FIG. 3, FIG. 4A and FIG. 4B, since the vibration cycle T of the object 50 under test does not exceed the pulse time δT of the stroboscopic pulse 312, the interference contrast of the vibratory interferometric signal decreases, resulting in image blurs (with lowered signal-to-noise ratio). Difficulty in calculating the exact positions with maximum interference intensity for vibratory interferometric signals will undermine the accuracy in reconstructing the three-dimensional profile of the object 50 under test.
Although the interference contrast of the vibratory interferometric signal can be enhanced by shortening the pulse time δT of the stroboscopic pulse 312, there is a limitation in such because the stroboscopic pulse 312 is not a mathematically ideal delta function. In view of the above, the conventional vibratory measurement method is not suitable for obtaining the surface profile of an object under high-frequency vibration.